# Modeling with Two Variable Equations and Inequalties

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## Objective

SWBAT create equations and inequalities in two variables to solve a real world problem.

#### Big Idea

Students will make a real life problem easier to understand by representing and solving it graphically.

## Launch

10 minutes

At the start of today's lesson I put students in pairs or groups of three and give them opener problem. I also project the problem up on the board.  Students will need to make sense of this problem, before they can solve it.  I allow students to take some time to read through the problem more than once and underline important pieces of information.  Without giving students any guidance, have them begin to attempt a solution in their groups.

As students work through the details of the problem, I monitor their progress and ask questions to help them get unstuck.  I try not to be too helpful when the students are working.  The struggle of understanding a problem will teach perseverance and will lead to good ideas later on in the lesson (MP1). I encourage students to communicate their ideas to their partners in a clear way during discussions. I also ask students not to erase anything that they try.  Student mistakes will help you to follow their thinking later on when you are assessing their work.

Students should come to the understanding that there are many correct solutions to this question. They need to begin to think about how they will show all of the solutions to the problem.  I help students to gain the understanding that there are two questions being asked.  One question is about an equation (exactly \$2000) and the other is about an inequality (at least \$1000).  I am on the lookout for groups that have written down equations and inequalities to help them solve the problem versus those who have simply written down ordered pairs or made a list.

## Investigation

25 minutes

Once each group has a solid plan you can give them the remaining pages of the solving_two_variable_equations investigation.  These questions will help formalize and guide their thoughts. It will also build on the discussions that they have already had in their partnerships. I try to leave some time in this segment to go over some key ideas presented in this investigation.

Here are my points of emphasis:

1) Question 2a and 2b connect the abstract concept of the coordinates on a line to actual numbers of shirts.  Once students graph the line later in the investigation, I tie back to this question to show them that the point in 2a is not on the line and the point in 2b is.

2) In question 3c and 3d, we continue to make a connection between the abstract linear function and the concrete situation that it represents.

3) In question 4d, once students have graphed their inequality, they should show an understanding that all of the points on the line and in the shaded area are solutions to the question.  Any combination in that shaded area would help the booster club raise more than \$1000.

## Closure

5 minutes

I will have students write the answer to this Ticket out the Door on a separate sheet of paper:

How will the progressive sale of T-shirts affect the number of sweatshirts that need to be sold or vice-versa?  Explain your answer.

The student answers will give me some insight into their understanding of the structure of a linear equation (MP7).